Uncertainty Quantification of Turbulence Model Coefficients via Latin Hypercube Sampling Method

The article is concerned with the propagation of uncertainties in the values of turbulence model coefficients and parameters in turbulent flows. These coefficients and parameters are obtained through experiments performed on elementary flows, and they are subject to uncertainty. In this work, the widely used $k-ɛ$ turbulence model is considered. It consists of model transport equations for the turbulence kinetic energy and the rate of turbulent dissipation. Both equations involve various model coefficients about which adequate knowledge is assumed known in the form of probability density functions. The study is carried out for a flow over a 2D backward-facing step configuration. The Latin Hypercube Sampling method is employed for the uncertainty quantification purposes as it requires a smaller number of samples compared to the conventional Monte Carlo method. The mean values are reported for the flow output parameters of interest along with their associated uncertainties. The results show that model coefficient variability has significant effects on the streamwise mean velocity in the recirculation region near the reattachment point and turbulence intensity along the free shear layer. The reattachment point location, pressure, and wall shear are also significantly influenced by the uncertainties of the coefficients.